## A Supplement to Fujino's Paper: On Isolated Log Canonical Singularities with Index One

J. Math. Sci. Univ. Tokyo
Vol. 19 (2012), No. 1, Page 135--138.

Ishii, Shihoko
A Supplement to Fujino's Paper: On Isolated Log Canonical Singularities with Index One
Let $E$ be the essential part of the exceptional locus of a good resolution of an isolated, log canonical singularity of index one. We describe the dimension of the dual complex of $E$ in terms of the Hodge type of $H^{n-1}(E,\o_E)$, which is one of the main results of the paper \cite{f} of Fujino. Our proof uses only an elementary classical method, while Fujino's argument depends on the recent development in minimal model theory.